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Abstract A rigorous geometric proof of the Lie theorem on nonlinear superposition rules for solutions of nonautonomous ordinary differential equations is given filling in all the gaps present in the… (More)

Various problems concerning the geometry of the space of Hermitian operators on a Hilbert space are addressed. In particular, we study the canonical Poisson and Riemann?Jordan tensors and the… (More)

Foreword: The birth and the long gestation of a project.- Some examples of linear and nonlinear physical systems and their dynamical equations.- Equations of the motion for evolution systems.- Linear… (More)

We analyze the global theory of boundary conditions for a constrained quantum system with classical configuration space a compact Riemannian manifold M with regular boundary Γ=∂M. The space ℳ of… (More)

Jacobi algebroids, i.e. graded Lie brackets on the Grassmann algebra associated with a vector bundle which satisfy a property similar to that of the Jacobi brackets, are introduced. They turn out to… (More)

In classical information geometry, the metric tensor and a dual pair of connections on the space of probability distributions may be obtained from a potential function.The metric is essentially… (More)

The geometrical description of a Hilbert space associated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields.… (More)

While there has been growing interest for noncommutative spaces in recent times, most examples have been based on the simplest noncommutative algebra: [xi, xj] = iθij. Here we present new classes of… (More)

We define quantum bi-Hamiltonian systems, by analogy with the classical case, as derivations in operator algebras which are inner derivations with respect to two compatible associative structures. We… (More)